Capacitance Calculator – Capacitor Values and Energy
Calculate capacitance, stored energy, and electric field for parallel plate, spherical, cylindrical, and series/parallel capacitor combinations.
Select the capacitor type, enter the required dimensions and dielectric constant, then click Calculate to see capacitance, stored energy, and electric field.
Capacitance Calculator – Capacitor Values and Energy
Calculate capacitance, stored energy, and electric field for parallel plate, spherical, cylindrical, and series/parallel capacitor combinations.
About the Capacitance Calculator
A capacitor stores electrical energy in an electric field between two conductors separated by a dielectric material. The capacitance C, measured in Farads (F), quantifies how much charge Q can be stored per unit voltage V: C = Q / V. This calculator handles the four most common capacitor geometries and the two standard combination rules.
The parallel plate capacitor is the simplest and most widely studied geometry. Two flat conducting plates of area A are separated by a gap d filled with a dielectric material with relative permittivity εᵣ. The capacitance is C = ε₀ × εᵣ × A / d, where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. Increasing plate area or dielectric constant increases capacitance; increasing separation decreases it. The electric field between the plates is uniform: E = V / d.
The spherical capacitor consists of two concentric spherical shells with inner radius r₁ and outer radius r₂. Its capacitance is C = 4πε₀εᵣ × (r₁ × r₂) / (r₂ − r₁). In the limit r₂ → ∞, this reduces to the capacitance of an isolated sphere: C = 4πε₀εᵣr₁, which models the self-capacitance of a conducting ball.
The cylindrical capacitor consists of two coaxial conducting cylinders of length L with inner radius r₁ and outer radius r₂. Its capacitance is C = 2πε₀εᵣL / ln(r₂ / r₁). This geometry models coaxial cables, where the inner conductor and outer sheath act as the two plates of a distributed capacitor along the cable length.
When capacitors are connected in series, the reciprocal of the total capacitance equals the sum of reciprocals: 1/C_total = 1/C₁ + 1/C₂ + 1/C₃. Series combination reduces total capacitance but increases the voltage rating. When connected in parallel, capacitances simply add: C_total = C₁ + C₂ + C₃. Parallel combination increases total capacitance while keeping the voltage rating of the lowest-rated component.
The energy stored in any charged capacitor is E = ½ × C × V², where V is the voltage across the capacitor. This energy is held in the electric field between the conductors and can be released rapidly — which is why capacitors are used in camera flashes, defibrillators, power factor correction, and energy-storage systems for electric vehicles.
Dielectric materials play a crucial role: their relative permittivity εᵣ (also called dielectric constant) multiplies the baseline air-gap capacitance. Common values are: vacuum/air ≈ 1.0, paper ≈ 3.5, glass ≈ 5–10, ceramic ≈ 100–10,000 for barium titanate, and PTFE (Teflon) ≈ 2.1. High-εᵣ ceramics allow very large capacitances in small packages, which is why ceramic capacitors are the most common type in modern electronics.
Capacitance Calculator Examples
Four examples covering each major capacitor type and combination.
| Configuration | Capacitance / Energy | Context |
|---|---|---|
| Parallel plate: A=0.01 m², d=0.001 m, εr=1.0, V=12 V | C ≈ 88.54 pF · E ≈ 6.37 nJ | Air-dielectric parallel plate at 12 V. Typical of a simple lab demonstration capacitor. |
| Spherical: r₁=0.05 m, r₂=0.06 m, εr=100, V=24 V | C ≈ 3.34 nF · E ≈ 962 nJ | Ceramic-dielectric spherical capacitor; high εr compensates for small size. |
| Cylindrical: r₁=0.02 m, r₂=0.025 m, L=0.1 m, εr=3.5, V=6 V | C ≈ 87.27 pF · E ≈ 1.57 nJ | Paper-dielectric coaxial geometry; models a short section of insulated coaxial cable. |
| Parallel combination: C₁=1 µF, C₂=2 µF, C₃=3 µF, V=12 V | C_total = 6 µF · E = 432 µJ | Three capacitors in parallel; total capacitance is the sum of all three values. |
How to Use the Capacitance Calculator
- Select the capacitor type from the dropdown: Parallel Plate, Spherical, Cylindrical, Series Combination, or Parallel Combination.
- Enter the required dimensions for the selected type. For parallel plate: area and separation; for spherical/cylindrical: inner and outer radii (plus length for cylindrical); for combinations: C1, C2, C3 values.
- Enter the dielectric constant (εr). Use 1.0 for air/vacuum, or the appropriate value for your dielectric material.
- Enter the voltage across the capacitor to calculate stored energy. Leave as zero if energy is not needed.
- Click 'Calculate' to see capacitance in Farads, stored energy in Joules, and electric field where applicable.
Frequently Asked Questions
What is the permittivity of free space (ε₀)?
The permittivity of free space, ε₀, is a fundamental physical constant equal to 8.854187817 × 10⁻¹² F/m (Farads per metre). It appears in all capacitance formulas and quantifies how easily an electric field can form in a vacuum. The relative permittivity (dielectric constant) εᵣ of any material is defined as its permittivity divided by ε₀, giving dimensionless values greater than or equal to 1.
How does a dielectric material increase capacitance?
When a dielectric material is placed between the capacitor plates, its polar molecules align with the applied electric field, creating an opposing polarisation field. This reduces the effective electric field for a given charge, allowing more charge to be stored at the same voltage — hence higher capacitance. The factor by which capacitance increases relative to vacuum is the dielectric constant εᵣ. Higher εᵣ materials store proportionally more energy.
When should I use series vs parallel capacitor combination?
Use series combination when you need a higher voltage rating or a smaller total capacitance than any single capacitor provides. Note that in series the total capacitance is always less than the smallest individual capacitor. Use parallel combination when you need larger total capacitance or to share current demand across multiple capacitors. Parallel combination keeps the voltage rating of the weakest capacitor as the limit.
What is the unit Farad and why are most practical capacitors in micro- or nano-Farads?
One Farad is the capacitance of a capacitor that stores one Coulomb of charge for every Volt across it. One Farad is an extremely large capacitance for most electronic applications — a 1 F parallel plate capacitor with air dielectric would require plates about the size of a football field separated by 1 mm. Practical capacitors used in electronics range from picofarads (pF, 10⁻¹² F) for RF circuits to microfarads (µF, 10⁻⁶ F) for power supply filters and millifarads to Farads for supercapacitors.
How is the electric field calculated inside a capacitor?
For a parallel plate capacitor with uniform field, E = V / d, where V is the voltage and d is the plate separation in metres. The result is in Volts per metre (V/m). For spherical and cylindrical capacitors the field is non-uniform and varies with radius; the calculator shows the field at the inner conductor surface, where the field is strongest, using E = V / (r₁ × ln(r₂/r₁)) for cylindrical and E = V × r₂ / (r₁ × (r₂ − r₁)) for spherical.
What are typical capacitance values for different capacitor types?
Ceramic capacitors: 1 pF to 100 µF; film capacitors: 1 nF to 100 µF; electrolytic capacitors: 1 µF to 100,000 µF; supercapacitors (EDLC): 0.1 F to thousands of Farads. The huge range reflects different dielectric materials, plate areas, and physical sizes. Ceramic capacitors in 0402 packages can now reach 10 µF by using high-εᵣ barium titanate ceramics with plate separations of just a few micrometres.